Research output: Contribution to journal › Article › peer-review
Outer automorphisms of sl(2), integrable systems, and mappings. / Tsyganov, A. V.
In: Theoretical and Mathematical Physics, Vol. 118, No. 2, 01.01.1999, p. 164-172.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Outer automorphisms of sl(2), integrable systems, and mappings
AU - Tsyganov, A. V.
PY - 1999/1/1
Y1 - 1999/1/1
N2 - Outer automorphisms of infinite-dimensional representations of the Lie algebra sl(2) are used to construct Lax matrices for integrable Hamiltonian systems and discrete integrable mappings. The known results are reproduced, and new integrable systems are constructed. Classical r-matrices corresponding to the Lax representation with the spectral parameter are dynamic. This scheme is advantageous because quantum systems naturally arise in the framework of the classical r-matrix Lax representation and the corresponding quantum mechanical problem admits a variable separation.
AB - Outer automorphisms of infinite-dimensional representations of the Lie algebra sl(2) are used to construct Lax matrices for integrable Hamiltonian systems and discrete integrable mappings. The known results are reproduced, and new integrable systems are constructed. Classical r-matrices corresponding to the Lax representation with the spectral parameter are dynamic. This scheme is advantageous because quantum systems naturally arise in the framework of the classical r-matrix Lax representation and the corresponding quantum mechanical problem admits a variable separation.
UR - http://www.scopus.com/inward/record.url?scp=0033242389&partnerID=8YFLogxK
U2 - 10.1007/BF02557309
DO - 10.1007/BF02557309
M3 - Article
AN - SCOPUS:0033242389
VL - 118
SP - 164
EP - 172
JO - Theoretical and Mathematical Physics (Russian Federation)
JF - Theoretical and Mathematical Physics (Russian Federation)
SN - 0040-5779
IS - 2
ER -
ID: 36285094